Editing Quantum Hall effect (section)

=== Transverse resistivity ===
From the classical relation of the transverse resistivity <math display="inline">\rho_{xy}=\frac{B}{en_{\rm 2D}}</math> and substituting <math display="inline">n_{\rm 2D}=\nu \frac{eB}{h}</math>  one finds out the quantization of the transverse resistivity and conductivity:
: <math>\rho_{xy}=\frac{h}{\nu e^2}\Rightarrow \sigma=\nu \frac{e^2}{h}</math>

One concludes then, that the transverse resistivity is a multiple of the inverse of the so-called conductance quantum <math>e^2/h</math> if the filling factor is an integer.  In experiments, however, plateaus are observed for whole plateaus of filling values <math>\nu</math>, which indicates that there are in fact electron states between the Landau levels. These states are localized in, for example, impurities of the material where they are trapped in orbits so they can not contribute to the conductivity. That is why the resistivity remains constant in between Landau levels. Again if the magnetic field decreases, one gets the classical result in which the resistivity is proportional to the magnetic field.